Estimating the Effective Reproduction Number of COVID-19 in United Kingdom
Louis Rossouw
2020-11-10
1 Introduction
This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various nations and other regions \(m\) of United Kingdom. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodolgy and assumptions are described in more detail here.
This paper and it’s results should be updated roughly daily and is available online.
As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was b0e60a113750ca2637ec52c0391763ecf8851ace.
2 Data
Data is obtained [3]. This contains the daily cases, hospital admissions and deaths for United Kingdom by various geographies. Here the data is accessed by specimen date, admission date and date of death.
Once history is built up an allowance for rate reported cases, admissions and deaths will be made. For now the data is cut-off a week prior to the last case date in the data. All data prior to 1 March 2020 are removed.
3 Methodology
The methodology is described in detail here.
4 Results by Nation
4.1 Cases
Below we plot cumulative case count on a log scale by nation:
Cumulative Cases by Nation
4.2 Admissions
Below we plot cumulative hospital admissions on a log scale.
Cumulative Admissions by Nation
4.3 Deaths
Below we plot the cumulative deaths by nation on a log scale:
Cumulative Deaths by Nation
4.4 Current \(R_{t,m}\) estimates by Nation
Below current (last weekly) \(R_{t,m}\) estimates are tabulated.
| Nation | Estimate Type | Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| England | cases | 130,658 | 2020-11-01 | 1.0 | 1.0 | 1.0 |
| England | admissions | 8,682 | 2020-11-01 | 1.1 | 1.2 | 1.2 |
| England | deaths | 1,660 | 2020-11-01 | 1.2 | 1.2 | 1.3 |
| Northern Ireland | cases | 4,977 | 2020-11-01 | 0.8 | 0.8 | 0.8 |
| Northern Ireland | admissions | 293 | 2020-11-01 | 0.8 | 0.9 | 1.0 |
| Northern Ireland | deaths | 67 | 2020-11-01 | 1.1 | 1.4 | 1.7 |
| Scotland | cases | 7,843 | 2020-11-01 | 0.8 | 0.9 | 0.9 |
| Scotland | admissions | 653 | 2020-11-01 | 0.8 | 0.9 | 1.0 |
| Scotland | deaths | 176 | 2020-11-01 | 1.2 | 1.3 | 1.5 |
| Wales | cases | 9,029 | 2020-11-01 | 1.0 | 1.1 | 1.1 |
| Wales | admissions | 612 | 2020-11-01 | 0.9 | 0.9 | 1.0 |
| Wales | deaths | 117 | 2020-11-01 | 1.0 | 1.2 | 1.4 |
Estimated Effective Reproduction Number by Nation
4.5 Maps of Effective Reproduction Number
Below we plot the current effective reproduction number on maps with boundaries provided by [4].
4.5.1 Cases
4.5.2 Admissions
4.5.3 Deaths
4.6 Graphs over Time
Below we plot results for each nation We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds 4.
4.6.1 England
4.6.2 Northern Ireland
4.6.3 Scotland
4.6.4 Wales
5 Results by Region
5.1 Cases
Below we plot cumulative case count on a log scale by region:
Cumulative Cases by Region
5.2 Deaths
Below we plot the cumulative deaths by region on a log scale:
Cumulative Deaths by Region
5.3 Current \(R_{t,m}\) estimates by Region
Below current (last weekly) \(R_{t,m}\) estimates are tabulated.
| Region | Estimate Type | Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| Northern Ireland | cases | 4,977 | 2020-11-01 | 0.8 | 0.8 | 0.8 |
| Northern Ireland | deaths | 67 | 2020-11-01 | 1.1 | 1.4 | 1.7 |
| Scotland | cases | 7,843 | 2020-11-01 | 0.8 | 0.9 | 0.9 |
| Scotland | deaths | 176 | 2020-11-01 | 1.2 | 1.3 | 1.5 |
| Wales | cases | 9,029 | 2020-11-01 | 1.0 | 1.1 | 1.1 |
| Wales | deaths | 117 | 2020-11-01 | 1.0 | 1.2 | 1.4 |
| East Midlands | cases | 13,343 | 2020-11-01 | 1.0 | 1.0 | 1.0 |
| East Midlands | deaths | 168 | 2020-11-01 | 1.0 | 1.2 | 1.4 |
| East of England | cases | 6,479 | 2020-11-01 | 0.9 | 1.0 | 1.0 |
| East of England | deaths | 104 | 2020-11-01 | 1.1 | 1.4 | 1.6 |
| London | cases | 13,027 | 2020-11-01 | 0.9 | 0.9 | 0.9 |
| London | deaths | 89 | 2020-11-01 | 0.9 | 1.1 | 1.3 |
| North East | cases | 7,842 | 2020-11-01 | 0.9 | 1.0 | 1.0 |
| North East | deaths | 143 | 2020-11-01 | 1.0 | 1.1 | 1.3 |
| North West | cases | 30,179 | 2020-11-01 | 0.9 | 0.9 | 0.9 |
| North West | deaths | 538 | 2020-11-01 | 1.1 | 1.2 | 1.3 |
| South East | cases | 10,826 | 2020-11-01 | 1.0 | 1.0 | 1.1 |
| South East | deaths | 93 | 2020-11-01 | 1.1 | 1.4 | 1.7 |
| South West | cases | 8,211 | 2020-11-01 | 1.0 | 1.0 | 1.1 |
| South West | deaths | 67 | 2020-11-01 | 1.1 | 1.4 | 1.7 |
| West Midlands | cases | 16,210 | 2020-11-01 | 1.1 | 1.1 | 1.1 |
| West Midlands | deaths | 170 | 2020-11-01 | 1.1 | 1.3 | 1.5 |
| Yorkshire and The Humber | cases | 23,299 | 2020-11-01 | 1.0 | 1.0 | 1.0 |
| Yorkshire and The Humber | deaths | 263 | 2020-11-01 | 1.1 | 1.2 | 1.3 |
Estimated Effective Reproduction Number by Region
5.4 Maps of Effective Reproduction Number
Below we plot the current effective reproduction number on maps with boundaries provided by [5].
5.4.1 Cases
5.4.2 Deaths
5.5 Graphs over Time
Below we plot results for each nation We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds 4.
5.5.1 Northern Ireland
5.5.2 Scotland
5.5.3 Wales
5.5.4 East Midlands
5.5.5 East of England
5.5.6 London
5.5.7 North East
5.5.8 North West
5.5.9 South East
5.5.10 South West
5.5.11 West Midlands
5.5.12 Yorkshire and The Humber
6 Results by NHS Region
6.1 Current \(R_{t,m}\) estimates by Region
Below current (last weekly) \(R_{t,m}\) estimates are tabulated.
| Region | Estimate Type | Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| Northern Ireland | admissions | 293 | 2020-11-01 | 0.8 | 0.9 | 1.0 |
| Scotland | admissions | 653 | 2020-11-01 | 0.8 | 0.9 | 1.0 |
| Wales | admissions | 612 | 2020-11-01 | 0.9 | 0.9 | 1.0 |
| East of England | admissions | 432 | 2020-11-01 | 1.1 | 1.2 | 1.3 |
| London | admissions | 908 | 2020-11-01 | 1.1 | 1.1 | 1.2 |
| North West | admissions | 2,100 | 2020-11-01 | 1.0 | 1.1 | 1.1 |
| South East | admissions | 624 | 2020-11-01 | 1.2 | 1.3 | 1.4 |
| South West | admissions | 544 | 2020-11-01 | 1.3 | 1.4 | 1.6 |
| Midlands | admissions | 1,821 | 2020-11-01 | 1.1 | 1.2 | 1.3 |
| North East and Yorkshire | admissions | 2,253 | 2020-11-01 | 1.1 | 1.2 | 1.2 |
Estimated Effective Reproduction Number by Region
6.2 Maps of Effective Reproduction Number
Below we plot the current effective reproduction number on maps with boundaries provided by [6].
6.3 Graphs over Time
Below we plot results for each nation We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds 4.
6.3.1 East of England
6.3.2 London
6.3.3 Midlands
6.3.4 North East and Yorkshire
6.3.5 North West
6.3.6 South East
6.3.7 South West
7 Results by Upper Tier Local Authority
7.1 Highest \(R_{t,m}\) as estimated using cases
Below we plot Upper Tier Local Authorities with the hghest reproduction numbers (providing they had at least 100 cases):
## Selecting by Rt_ui_95| Upper Tier Local Authority | Estimate Type | Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| Vale of Glamorgan | cases | 221 | 2020-11-01 | 1.2 | 1.5 | 1.7 |
| Kingston upon Hull, City of | cases | 1,231 | 2020-11-01 | 1.3 | 1.4 | 1.5 |
| Denbighshire | cases | 129 | 2020-11-01 | 1.1 | 1.3 | 1.6 |
| Powys | cases | 156 | 2020-11-01 | 1.1 | 1.3 | 1.5 |
| Medway | cases | 398 | 2020-11-01 | 1.1 | 1.3 | 1.4 |
| Dudley | cases | 1,171 | 2020-11-01 | 1.2 | 1.3 | 1.4 |
| Shropshire | cases | 586 | 2020-11-01 | 1.1 | 1.2 | 1.3 |
| Gloucestershire | cases | 719 | 2020-11-01 | 1.1 | 1.2 | 1.3 |
| Blaenau Gwent | cases | 392 | 2020-11-01 | 1.1 | 1.2 | 1.3 |
| Swindon | cases | 384 | 2020-11-01 | 1.1 | 1.2 | 1.3 |
| North East Lincolnshire | cases | 783 | 2020-11-01 | 1.1 | 1.2 | 1.3 |
| Luton | cases | 481 | 2020-11-01 | 1.1 | 1.2 | 1.3 |
| Merthyr Tydfil | cases | 456 | 2020-11-01 | 1.0 | 1.2 | 1.3 |
| Slough | cases | 328 | 2020-11-01 | 1.0 | 1.2 | 1.3 |
| North Lincolnshire | cases | 445 | 2020-11-01 | 1.1 | 1.2 | 1.3 |
| North Somerset | cases | 388 | 2020-11-01 | 1.0 | 1.1 | 1.3 |
| Central Bedfordshire | cases | 287 | 2020-11-01 | 1.0 | 1.1 | 1.3 |
| Carmarthenshire | cases | 327 | 2020-11-01 | 1.0 | 1.1 | 1.3 |
| Havering | cases | 541 | 2020-11-01 | 1.0 | 1.1 | 1.2 |
| Wrexham | cases | 433 | 2020-11-01 | 1.0 | 1.1 | 1.2 |
| Newport | cases | 305 | 2020-11-01 | 1.0 | 1.1 | 1.3 |
| Southampton | cases | 410 | 2020-11-01 | 1.0 | 1.1 | 1.2 |
| Torbay | cases | 230 | 2020-11-01 | 1.0 | 1.1 | 1.3 |
| Bedford | cases | 203 | 2020-11-01 | 1.0 | 1.1 | 1.3 |
| Reading | cases | 237 | 2020-11-01 | 1.0 | 1.1 | 1.3 |
7.2 Map of Effective Reproduction Number (Cases)
Below we plot the current effective reproduction number estimated from case data on maps with boundaries provided by [7].
7.3 Map over by week since start of the year (experimental)
Below the reproduction number by week for each Upper Tier Local Authority is animated:
8 Detailed Results
Detailed output are saved to a comma-separated value file. The file can be found here.
9 Discussion
Limitation of this method to estimate \(R_{t,m}\) are noted in [1]
- It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
- It relies on an assumed generation interval assumptions.
- The size of the time window can affect the volatility of results.
- Results are time lagged with regards to true infection, more so in the case of the use of deaths.
- It’s sensitive to changes in case (or death) detection.
- The generation interval may change over time.
Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths. It may well be that some catch-up in reported deaths is exaggerating the estimates for October.
Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.
Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.
Having said all the above it would appear that the effective reproduction number was reasonably high in United Kingdom from middle April to middle July. From middle July the figures seems to have decreased well below 1. However since middle September figures have been near 1 and in October these seem to have shifted above 1.
11 Digital boundaries
Office for National Statistics licensed under the Open Government Licence v.3.0
Contains OS data © Crown copyright and database right 2020
References
[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133
[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim
[3] Office for National Statistics, “Official UK Coronavirus Dashboard,” 2020. [Online]. Available: https://coronavirus.data.gov.uk. [Accessed: 07-Nov-2020]
[4] Office for National Statistics, “Countries (December 2019) Boundaries UK BUC,” 09-Oct-2017. [Online]. Available: https://geoportal.statistics.gov.uk/search?collection=Dataset. [Accessed: 07-Nov-2020]
[5] Office for National Statistics, “NUTS Level 1 (January 2018) Ultra Generalised Clipped Boundaries in the United Kingdom,” 31-Jul-2017. [Online]. Available: https://geoportal.statistics.gov.uk/datasets/nuts-level-1-january-2018-ultra-generalised-clipped-boundaries-in-the-united-kingdom. [Accessed: 07-Nov-2020]
[6] Office for National Statistics, “NHS England Regions (April 2020) Boundaries EN BUC,” 13-May-2020. [Online]. Available: https://geoportal.statistics.gov.uk/search?collection=Dataset. [Accessed: 07-Nov-2020]
[7] Office for National Statistics, “Counties and Unitary Authorities (December 2019) Boundaries UK BUC,” 11-Mar-2020. [Online]. Available: https://geoportal.statistics.gov.uk/datasets/counties-and-unitary-authorities-december-2019-boundaries-uk-buc. [Accessed: 07-Nov-2020]